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  • Cryptographie

    Vendredi 15 décembre 2017 11:00-12:00 - Christina Boura - UVSQ

    Two Notions of Differential Equivalence on Sboxes

    Résumé : The security of symmetric constructions, such as block ciphers and hash functions, heavily relies on the choice of the Sboxes, whose main role is to provide non-linearity. In this work we discuss two notions of differential equivalence on Sboxes. First, we introduce the notion of DDT-equivalence which applies to vectorial Boolean functions that share the same difference distribution table (DDT). Next, we compare this notion, to what we call the γ-equivalence, applying to vectorial Boolean functions whose DDTs have the same support. We discuss the relation between these two equivalence notions and show how they behave for two classical equivalences for vectorial Boolean functions, namely the Affine Equivalence and the CCZ equivalence. We provide further an algorithm for computing the DDT-equivalence and the γ-equivalence classes for a given function and we study the sizes of these classes for some important families of Sboxes. Finally, we prove a result that shows that the rows of the DDT of an APN permutation are pairwise distinct.
    This is a joint work with Anne Canteaut, Jérémy Jean and Valentin Suder.

    Lieu : Bât. Descartes, Salle 301

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